The number of integers greater than 6000 that can be formed using the digits 3,5,6,7 and 8 without repetition, is

Options

A. 120
B. 72
C. 216
D. 192

Answer

D

Explanation

There are 5-digits viz 3, 5, 6, 7 and 8. Integers gerater than 6000, formed by the given digits, are four digit numbers as well as five digit integers.
Number of five digit numbers =5!=120
Four digit integers greater than 6000 may have any one of the digits 6, 7 and 8 at thousands place and the remaining three places can be filled from the remaining 4 digits in `""^(4)C_(3)xx3!` ways. Therefore,
Number of four digit integers greater than 6000 is `3xx^(4)C_(3)xx3!`
Hence, requird number of integers `=120+3xx^(4)C_(3)xx3!""192`